WK4AssgnWillisK9.doc - Running head PROPORTIONAL REASONING 1 Proportional Reasoning Activity Kimberly M Willis Walden University Amy Gaskins Algebraic

# WK4AssgnWillisK9.doc - Running head PROPORTIONAL REASONING...

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Running head: PROPORTIONAL REASONING 1 Proportional Reasoning Activity Kimberly M. Willis Walden University Amy Gaskins Algebraic Reasoning, Functions, and Equations MATH- 6553A July 27, 2014

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PROPORTIONAL REASONING 2 Proportional Reasoning Proportional reasoning cannot be taught (or learned) in one lesson but must be developed through activities. Like equivalence, proportional reasoning is considered to be a unifying theme in mathematics because it is not simply how to set up a proportion to solve a problem but rather a way of reasoning about situations (Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M.. 2013). Because proportional reasoning requires a true understanding, rather than simply using an algorithm, this ability is developed throughout the course of several years beginning in elementary school. In sixth grade, students are still developing an understanding of ratios and proportions. I find it very important for students to use manipulatives and a variety of strategies to solve the problems. I try to stay away from the algorithm as long as possible because I feel that the algorithm is not really necessary if the students have a strong understanding of proportions. In this lesson, I started by giving students cubes with two different colors (I gave blue and black). I presented them with the problem, A package of pens contains one blue pen and four black pens. Use your cubes to model this situation. I figured this was a good way to introduce probability. Students have set up a ratio of blue to black pens without even realizing it. Next, I took it one step further and asked the students what would happen if there were two packs. Some students immediately wanted to tell me that I would have twice as many blue and black pens. I had students model their thoughts using the cubes. Students have now found equivalent ratios still without even mentioning ratios or proportions. Next, I allowed the students a little more freedom by asking them what other amounts of each color pen they would have if they bought more packs. I allowed the students time to experiment and come up with several different answers. Students then had the opportunity to share different answers with their classmates and
PROPORTIONAL REASONING 3 we kept a list on the board on chart paper. I save this list so that we can refer back to it in future lesssons. The last part of this first activity required students to work backwards to solve this problem. They were challenged to find out how many blue pens the secretary ordered if she ordered a total of 42 pens. Students who are able to study mathematics and work inversely to make links with their prior knowledge have a much deeper understanding of the material they are learning. As the students worked together on similar scenarios, I encouraged them to use different methods. In the beginning, students used the cubes. I then began to see students using drawings, symbols, repeated addition, multiplication and division. I was excited with the number of methods they used.

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